Han-Gook vs Korea

Han-Gook and Korea both are nouns.

Word	Noun	Adjective	Verb	Adverb
Han-Gook	Yes	No	No	No
Korea	Yes	No	No	No

As nouns, Han-Gook and Korea are synonyms defined as:

Han-Gook and Korea: an Asian peninsula (off Manchuria) separating the Yellow Sea and the Sea of Japan; the Korean name is Dae-Han-Min-Gook or Han-Gook

Other synonyms of Han-Gook include Dae-Han-Min-Gook, Korean Peninsula.

Han-Gook (noun)	Korea (noun)
an Asian peninsula (off Manchuria) separating the Yellow Sea and the Sea of Japan; the Korean name is Dae-Han-Min-Gook or Han-Gook	an Asian peninsula (off Manchuria) separating the Yellow Sea and the Sea of Japan; the Korean name is Dae-Han-Min-Gook or Han-Gook